The electric current in a certain circuit is given by ##d^2 I/dt^2## + 4dI/dt + 2504I = 110. If I = 0 and dI/dt = 0 when t = 0, find I in terms of t.
The solution is attached in the TheProblemAndSolution.jpg file (along with the problem again).
I(t) = c_1 exp((a + ib)t) + c_2 exp((a – ib)t) = c_3 exp(at) cos(bt) + c_4 exp(at) sin(bt)
The Attempt at a Solution
I found the general solution to the homogeneous equation (that does not involve the particular solution). My confusion is about the particular solution. I know that I must find the particular solution and add it to the general solution to the homogeneous version of this differential equation but, I'm a little confused as to how I am supposed to know that I(1) = 110/2504 is the initial value condition (so that I can use it to find the particular solution and, then, the general solution to the entire differential equation)?
Any input would be greatly appreciated!